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  • Open Access

    ARTICLE

    Analysis of 3D Anisotropic Solids Using Fundamental Solutions Based on Fourier Series and the Adaptive Cross Approximation Method

    R. Q. Rodríguez1,2, C. L. Tan2, P. Sollero1, E. L. Albuquerque3

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 359-372, 2014, DOI:10.3970/cmes.2014.102.359

    Abstract The efficient evaluation of the fundamental solution for 3D general anisotropic elasticity is a subject of great interest in the BEM community due to its mathematical complexity. Recently, Tan, Shiah, andWang (2013) have represented the algebraically explicit form of it developed by Ting and Lee (Ting and Lee, 1997; Lee, 2003) by a computational efficient double Fourier series. The Fourier coefficients are numerically evaluated only once for a specific material and are independent of the number of field points in the BEM analysis. This work deals with the application of hierarchical matrices and low rank approximations, applying the Adaptive Cross… More >

  • Open Access

    ARTICLE

    A (Constrained) Microstretch Approach in Living Tissue Modeling: a Numerical Investigation Using the Local Point Interpolation – Boundary Element Method

    Jean-Philippe Jehl1, Richard Kouitat Njiwa2

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.5, pp. 345-358, 2014, DOI:10.3970/cmes.2014.102.345

    Abstract Extended continuum mechanical approaches are now becoming increasingly popular for modeling various types of microstructured materials such as foams and porous solids. The potential advantages of the microcontinuum approach are currently being investigated in the field of biomechanical modeling. In this field, conducting a numerical investigation of the material response is evidently of paramount importance. This study sought to investigate the potential of the (constrained) microstretch modeling method. The problem’s field equations have been solved by applying a numerical approach combining the conventional isotropic boundary elements method with local radial point interpolation. Our resulting numerical examples demonstrated that the model… More >

  • Open Access

    ARTICLE

    Using Eulerlets to Give a Boundary Integral Formulation in Euler Flow and Discussion on Applications

    Edmund Chadwick1, Apostolis Kapoulas

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.4, pp. 331-343, 2014, DOI:10.3970/cmes.2014.102.331

    Abstract Boundary element models in inviscid (Euler) flow dynamics for a manoeuvring body are difficult to formulate even for the steady case; Although the potential satisfies the Laplace equation, it has a jump discontinuity in twodimensional flow relating to the point vortex solution (from the 2π jump in the polar angle), and a singular discontinuity region in three-dimensional flow relating to the trailing vortex wake. So, instead models are usually constructed bottom up from distributions of these fundamental solutions giving point vortex thin body methods in two-dimensional flow, and panel methods and vortex lattice methods in three-dimensional flow amongst others. Instead,… More >

  • Open Access

    ARTICLE

    Fatigue Crack Growth Reliability Analysis by Stochastic Boundary Element Method

    Xiyong Huang1, M. H. Aliabadi2, Z. Sharif Khodaei3

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.4, pp. 291-330, 2014, DOI:10.3970/cmes.2014.102.291

    Abstract In this paper, a stochastic dual boundary element formulation is presented for probabilistic analysis of fatigue crack growth. The method involves a direct differentiation approach for calculating boundary and fracture response derivatives with respect to random parameters. Total derivatives method is used to obtain the derivatives of fatigue parameters with respect to random parameters. First- Order Reliability Method (FORM) is applied to evaluate the most probable point (MPP). Opening mode fatigue crack growth problems are used as benchmarks to demonstrate the performance of the proposed method. More >

  • Open Access

    ARTICLE

    Inverse Green Element Solutions of Heat Conduction Using the Time-Dependent and Logarithmic Fundamental Solutions

    Akpofure E. Taigbenu1

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.4, pp. 271-289, 2014, DOI:10.3970/cmes.2014.102.271

    Abstract The solutions to inverse heat conduction problems (IHCPs) are provided in this paper by the Green element method (GEM), incorporating the logarithmic fundamental solution of the Laplace operator (Formulation 1) and the timedependent fundamental solution of the diffusion differential operator (Formulation 2). The IHCPs addressed relate to transient problems of the recovery of the temperature, heat flux and heat source in 2-D homogeneous domains. For each formulation, the global coefficient matrix is over-determined and ill-conditioned, requiring a solution strategy that involves the least square method with matrix decomposition by the singular value decomposition (SVD) method, and regularization by the Tikhonov… More >

  • Open Access

    ARTICLE

    Direct Volume-to-Surface Integral Transformation for 2D BEM Analysis of Anisotropic Thermoelasticity

    Y.C. Shiah1, Chung-Lei Hsu1, Chyanbin Hwu1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.4, pp. 257-270, 2014, DOI:10.3970/cmes.2014.102.257

    Abstract As has been well documented for the boundary element method (BEM), a volume integral is present in the integral equation for thermoelastic analysis. Any attempt to directly integrate the integral shall inevitably involve internal discretization that will destroy the BEM’s distinctive notion as a true boundary solution technique. Among the schemes to overcome this difficulty, the exact transformation approach is the most elegant since neither further approximation nor internal treatments are involved. Such transformation for 2D anisotropic thermoelasticity has been achieved by Shiah and Tan (1999) with the aid of domain mapping. This paper revisits this problem and presents a… More >

  • Open Access

    ARTICLE

    A Boundary Element - Response Matrix Method for 3D Neutron Diffusion and Transport Problems

    V. Giusti 1, B. Montagnini 1

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.3, pp. 229-255, 2014, DOI:10.3970/cmes.2014.102.229

    Abstract An application of a 3D Boundary Element Method (BEM), coupled with the Response Matrix (RM) technique, to solve the neutron diffusion and transport equations for multi-region domains is presented. The discussion is here limited to steady state problems, in which the neutrons have a wide energy spectrum, which leads to systems of several diffusion or transport equations. Moreover, the number of regions with different physical constants can be very large. The boundary integral equations concerning each region are solved via a polynomial moment expansion and, taking advantage of suitable recurrence formulas, the multi-fold integrals there involved are reduced to single… More >

  • Open Access

    ARTICLE

    Solving Embedded Crack Problems Using the Numerical Green’s Function and a meshless Coupling Procedure: Improved Numerical Integration

    E.F. Fontes Jr1, J.A.F. Santiago1, J.C.F. Telles1

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.3, pp. 211-228, 2014, DOI:10.3970/cmes.2014.102.211

    Abstract An iterative coupling procedure using different meshless methods is presented to solve linear elastic fracture mechanic (LEFM) problems. The domain of the problem is decomposed into two sub-domains, where each one is addressed using an appropriate meshless method. The method of fundamental solutions (MFS) based on the numerical Green’s function (NGF) procedure to generate the fundamental solution has been chosen for modeling embedded cracks in the elastic medium and the meshless local Petrov-Galerkin (MLPG) method has been chosen for modeling the remaining sub-domain. Each meshless method runs independently, coupled with an iterative update of interface variables to achieve the final… More >

  • Open Access

    ARTICLE

    Friction and Wear Modelling in Fiber-Reinforced Composites

    L. Rodríguez-Tembleque1, M.H. Aliabadi2

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.3, pp. 183-210, 2014, DOI:10.3970/cmes.2014.102.183

    Abstract This work presents new contact constitutive laws for friction and wear modelling in fiber-reinforced plastics (FRP). These laws are incorporated to a numerical methodology which allows us to solve the contact problem taking into account the anisotropic tribological properties on the interfaces. This formulation uses the Boundary Element Method for computing the elastic influence coefficients. Furthermore, the formulation considers micromechanical models for FRP that also makes it possible to take into account the fiber orientation relative to the sliding direction, the fiber volume fraction, the aspect ratio of fibers, or the fiber arrangement. The proposed contact and wear laws, as… More >

  • Open Access

    ARTICLE

    A Wavelet Method for Solving Bagley-Torvik Equation

    Xiaomin Wang1,2

    CMES-Computer Modeling in Engineering & Sciences, Vol.102, No.2, pp. 169-182, 2014, DOI:10.3970/cmes.2014.102.169

    Abstract In this paper, an efficient and robust wavelet Laplace inversion method of solving the fractional differential equations is proposed. Such an inverse function can be applied to any reasonable function categories and it is not necessary to know the properties of original function in advance. As an example, we have applied the proposed method to the solution of the Bagley–Torvik equations and Numerical examples are given to demonstrate the efficiency and accuracy of the proposed. More >

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